{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T04:36:03Z","timestamp":1787373363597,"version":"build-2736575974"},"reference-count":43,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/100012554","name":"Hubei Provincial Department of Education","doi-asserted-by":"publisher","award":["T201302"],"award-info":[{"award-number":["T201302"]}],"id":[{"id":"10.13039\/100012554","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61471275"],"award-info":[{"award-number":["61471275"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61625305"],"award-info":[{"award-number":["61625305"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2020,1]]},"abstract":"<jats:p>This paper considers the identification of a rational transfer function with sparse coefficients, under a pair of pulse and Takenaka--Malmquist (TM) bases and from a limited number of linear frequency domain measurements. We propose to concatenate pulse and TM basis functions in the representation of the transfer function, and prove the uniqueness of the sparse representation. We provide the sufficient condition under which the sparse system can be identified by $\\ell_1$ optimization from random samples with high probability, and also provide the computation algorithm. Numerical examples show that the concatenated pulse and TM bases give a much sparser representation, with much lower reconstruction order compared to using only pulse basis functions and less dependency on the knowledge of the true system poles compared to using only TM basis functions.<\/jats:p>","DOI":"10.1137\/18m1217474","type":"journal-article","created":{"date-parts":[[2020,3,30]],"date-time":"2020-03-30T15:32:50Z","timestamp":1585582370000},"page":"965-985","source":"Crossref","is-referenced-by-count":5,"title":["Sparse System Identification in Pairs of Pulse and Takenaka--Malmquist Bases"],"prefix":"10.1137","volume":"58","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6066-5125","authenticated-orcid":true,"given":"Dan","family":"Xiong","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4331-0565","authenticated-orcid":true,"given":"Li","family":"Chai","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jingxin","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2020,3,30]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"S. Boyd and L. Vandenberghe,\n                      Convex Optimization\n                      , Cambridge University Press, 2004.","DOI":"10.1017\/CBO9780511804441"},{"key":"atypb2","unstructured":"E. Cand\u00e8s and J. Romberg,\n                      \n                        $\\ell$1-\n                        magic\n                        : Recovery of Sparse Signals via Convex Programming\n                      \n                      , Technical report, Caltech, Pasadena, CA, 2005,https:\/\/statweb.stanford.edu\/~candes\/software\/l1magic."},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2005.862083"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.20124"},{"key":"atypb5","unstructured":"J. Chen and G. X. Gu,\n                      Control-Oriented System Identification: An $H_{\\infty}$ Approach\n                      , John Wiley & Sons, New York, 2000."},{"key":"atypb6","first-page":"251","author":"Chen J.","year":"1992","journal-title":"IEEE"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1137\/S003614450037906X"},{"key":"atypb8","first-page":"3125","author":"Chen Y.","year":"2009","journal-title":"Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1109\/78.740121"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2017.10.007"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2006.871582"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0437847100"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2002.801410"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2003.820031"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2009.2024736"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1109\/9.90229"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012902405340"},{"key":"atypb18","doi-asserted-by":"crossref","unstructured":"P. S. C. Heuberger, P. M. J. van den Hof, and B. Wahlberg, eds.\n                      Modelling and Identification with Rational Orthogonal Basis Functions\n                      , Springer-Verlag, London, 2005.","DOI":"10.1007\/1-84628-178-4"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2011.02.013"},{"key":"atypb20","doi-asserted-by":"crossref","unstructured":"T. Katayama,\n                      Subspace Methods for System Identification\n                      , Springer-Verlag London, 2005.","DOI":"10.1007\/1-84628-158-X"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2010.2090874"},{"key":"atypb22","unstructured":"L. Ljung,\n                      System Identification: Theory for the User\n                      , 2nd ed., Prentice-Hall, Englewood Cliffs, NJ, 1999."},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1016\/0005-1098(81)90085-6"},{"key":"atypb24","first-page":"793","volume":"2","author":"Malioutov D. M.","year":"2004","journal-title":"Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1109\/9.718626"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539792240406"},{"key":"atypb27","first-page":"381","author":"Ninness B.","year":"1996","journal-title":"Proceedings of the IFAC World Congress"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1109\/9.566661"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1016\/j.ifacol.2015.09.066"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1109\/9.333769"},{"key":"atypb31","first-page":"1","volume":"9","author":"Rauhut H.","year":"2010","journal-title":"Radon Ser. Comput. Appl. Math."},{"key":"atypb32","first-page":"3742","author":"Slavakis K.","year":"2010","journal-title":"Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing"},{"key":"atypb33","first-page":"2144","author":"Tivive F. H. C.","year":"2013","journal-title":"Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing"},{"key":"atypb34","doi-asserted-by":"crossref","unstructured":"R. T\u00f3th, B. M. Sanandaji, K. Poolla, and T. L. Vincent,\n                      Compressive system identification in the linear time-invariant framework\n                      , in 2011 50th IEEE Conference on Decision and Control and European Control Conference, 2011, pp. 783-790.","DOI":"10.1109\/CDC.2011.6160383"},{"key":"atypb35","unstructured":"G. Vairetti, T. van Waterschoot, M. Moonen, M. Catrysse, and S. H. Jensen,\n                      Sparse linear parametric modeling of room acoustics with Orthonormal Basis Functions\n                      , in 2014 22nd European Signal Processing Conference, 2014, pp. 1-5."},{"key":"atypb36","doi-asserted-by":"publisher","DOI":"10.1109\/9.76361"},{"key":"atypb37","doi-asserted-by":"publisher","DOI":"10.1109\/9.293196"},{"key":"atypb38","doi-asserted-by":"publisher","DOI":"10.1016\/0005-1098(95)00198-0"},{"key":"atypb39","doi-asserted-by":"crossref","unstructured":"D. Xiong, L. Chai, and J. Zhang,\n                      Sparse system identification using orthogonal rational functions\n                      , in Proceedings of the 11th World Congress on Intelligent Control and Automation, 2014, pp. 2340-2345.","DOI":"10.1109\/WCICA.2014.7053087"},{"key":"atypb40","doi-asserted-by":"crossref","unstructured":"D. Xiong, L. Chai, and J. Zhang,\n                      Compressed identification by sparse sampled frequency data\n                      , in Proceedings of the 30th Chinese Control and Decision Conference, 2018, pp. 3842-3846.","DOI":"10.1109\/CCDC.2018.8407790"},{"key":"atypb41","first-page":"4364","author":"Xiong D.","year":"2018","journal-title":"Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing"},{"key":"atypb42","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2019.07.004"},{"key":"atypb43","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2011.07.022"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/18M1217474","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:45:54Z","timestamp":1787316354000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/18M1217474"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1]]},"references-count":43,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2020,1]]}},"alternative-id":["10.1137\/18M1217474"],"URL":"https:\/\/doi.org\/10.1137\/18m1217474","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1]]}}}